When seeing two friends inviting each other, who could tell whether they are friends because they invite each other regularly, or if they invite each other regularly because they are friends? Such questions are common in systems where interactions occur over a social network. Obviously, interactions happen preferentially between socially connected individuals, but new ties are also created or reinforced through interactions. Understanding the mechanisms driving the evolution of these systems is an active field of research.
Most of the time, the social network is unknown and one can only record the interactions over time using various kinds of sensors. In such settings, a classical problem consists in infering the network from traces of interactions. With the developement of GPS and Bluetooth equiped devices such as smart phones, interaction data get more and more available, and there is a growing need to design efficient algorithms to infer the underlying relationships between entities. Alternatively, one may also study the opposite problem where the network is known and one wishes to infer associated interactions. Solving this kind of problems have various applications from trafic simulation to anomaly detection. Nonetheless, these problems are difficult to solve, and even difficult to study because of the lack of suitable data sources. We believe that better understanding the underlying mechanisms at play in such complex systems is a useful step within this line of work.
In this paper, we thus investigate the interplay between social ties and financial transactions using real data from a specific cryptocurrency. Similarly to friends inviting each other, we wish to better understand whether transactions occur between individuals who were already socially connected, or if individuals build a new tie because they are involved in regular trades. Studying these questions is often challenging because financial transactions are often considered as sensitive data, and rarely made public; even when they are, interactions are anonymized.
In 2008, the blockchain technology (Nakamoto 2009) opened the doors to new virtual currencies which do not rely on a central authority. Transactions are written in a public distributed ledger, such that anybody can obtain the full list of transactions. Since then, the number and diversity of applications relying on the blockchain has been continuously growing (Al-Saqaf and Seidler 2017; Hileman and Rauchs 2017). Although Bitcoin is still a benchmark cryptocurrency (Hileman and Rauchs 2017; Gohwong 2018), many new currencies relying on different kinds of blockchains have been introduced since then (Gohwong 2018). Most provide (to some extent) anonymity to the entities making transactions. Indeed, users of these systems are often encouraged to create a new address when they want to make a new transaction, making the association of users and addresses a problem on its own (Meiklejohn et al. 2013; Remy et al. 2018). Some heuristics have been proposed to tackle this challenge but they mostly work for big users and they are difficult to assess. In addition, even if users were identified properly, underlying social ties would remain unknown.
The \(\breve {G}1\) (BL et al. 2017) cryptocurrency under study in this paper relies on explicit social ties to strengthen the robustness of the system. It maintains an accurate network of identified users with reliable social ties, and uses it for monetary growth. This offers a unique opportunity to study the interplay between financial transactions and social ties between human beings of a specific community.
Related Work
Inferring relations from interactions
Scientific works tackling the general problem of inferring a network of social relationships from a sequence of interactions span several domains from sociology to computer science. With the increase of geotagged data availability due to the popularization of smart phones and other GPS equipped devices, a large portion of these studies focuses on the inference of social ties from mobility traces. Indeed, social networks are embedded in geography such that it is commonly assumed that interacting probability increases with physical proximity. For instance, the authors of Toole et al. (2015) use a call detail records (CDR) to explore the interplay between mobility and social ties, while the authors of Xu et al. (2019) rely on transactions made through student ID cards to build the students’ social network.
It is well-known that all social relationships are not equivalent (Bapna et al. 2017; Xiang et al. 2010). Indeed, they can, among other things, be of different nature and have different strength. Being able to not only infer social ties from interactions, but also quantify their nature and strength is a key challenge within this line of work. In this direction, the authors of Gelardi et al. (2019) study the interactions in a group of baboons in which they observe proximity and grooming as bounding activities. Similarly, the authors of Kobayashi et al. (2019) present a method to filter strong ties from temporal networks of interactions. Their method computes for each pair of nodes the distribution of their number of interactions in a null model based on node activities. Significant pairs of nodes are thus defined as those with a number of interactions that cannot be explained by the null model.
Slightly different studies aim at predicting missing links of a network from known links or other external features. For example, the authors of Crandall et al. (2010) use the proximity, in space and time, of geo-tagged photographs over the Flickr social network to infer the likelihood of a social tie between users. This paper shows that this probability increases by orders of magnitudes as the number of co-locations increases. Focusing on topological features, the authors of Hristova et al. (2016) explore the combined effect of multiple social networks for link prediction. More precisely, they represent social ties as a multiplex network where each layer represents a specific social platform, and they show how this additional information can be used to improve link prediction.
In Khosravi et al. (2013), the authors investigate link strength prediction in a social network based on social transactions (likes, comments, etc). They propose a new type of multiple-matrix factorization model for incorporating a transaction matrix between users, and test their method on Cloob (Cloob), a popular Iranian social network where users can rate their friendship relationships.
Inferring interactions from relations
If inferring the network of relationships (or missing links of this network) from traces of interactions is often studied, the inverse problem of simulating traces of interactions from the network is also an interesting area of research. In Barrat et al. (2013) for example, the authors propose a procedure to generate dynamical networks from any weighted directed graph. This graph is considered as the accumulation of paths between its nodes, and the proposed procedure unfolds these paths using random walks of variable lengths. The authors show that their approach is able to generate dynamical networks with bursty, repetitive, or correlated behaviors.
The case of financial transactions
Pioneering work studying both the nature and strength of social ties as well as the way people make transactions can be found in social sciences. In Zelizer (1996) for example, the authors propose to split payements into three categories: gifts, entitlements, and compensations, and show that each category corresponds to a specific set of social relationships and systems of meanings.
More recently, the authors of Martens and Provost (2011) use real but anonymized transaction records to infer a pseudo-social network of users in which two users are connected if they transfered money to the same entity. Then, they use this pseudo-social network for social targeting and obtain better performances than traditional models.
To the best of our knowledge, there is no previous work studying financial transactions and social interactions simultaneously from a reliable data source, even in specific settings. The recent development of cryptocurrencies is creating new opportunities for this kind of studies. Contrary to transactions relying on usual payment methods, blockchain based transactions are public and can be analyzed freely as long as the blockchain itself is public. In Kondor et al. (2014), for instance, the authors extract the transactions from the Bitcoin blockchain and build the network of transactions. They provide a graph-based analysis of this network and show that linear preferential attachment drives its growth. In Popuri and Gunes (2016) the authors study the network of transactions of both Bitcoin and Litecoin, while the authors of Maesa et al. (2019) recently studied the structure of the Bitcoin users graph, exhibiting a bow tie like structure between its components. In Kim et al. (2016), the authors analyzed user comments in online communities of Bitcoin, Ethereum, and Ripple to predict the price and number of transactions in these cryptocurrencies.
The main limitation is often that, in most of these systems, most public keys are used only once such that there is no obvious way to link real users to the set of keys they used to make transactions (Meiklejohn et al. 2013; Remy et al. 2018). In addition, even if users were identified properly, underlying social ties would remain unknown.
Our contribution
In this paper, we study a specific cryptocurrency which offers both a recording of transactions and of social bounds between identified human beings. This means that we know exactly who sent money to whom and when. Our main objective is to understand the interplay between these transactions and social ties between users.
More precisely, we first explore whether users start making transactions before creating a tie, or if they tend to make transactions with people they are already friends with. Going further, we study the different neighborhood structures and their evolution over time. We tackle questions such as: Are my transaction partners the same as my friends? How do my friends exchange between them compared to my transaction partners? Are my friends and transaction partners more and more homogeneous over time?
As we will see in “Dataset and link stream modeling” section, although the data is rather simple at first glance, the proper modeling of interactions is challenging and no unique, commonly accepted approach exists. We leverage here the recently introduced link stream model, which captures both the temporal and structural nature of data (Latapy et al. 2017; Latapy et al. 2019). We start our analysis with basic metrics targetting the questions above and we define link stream concepts as we need them in the analysis.
Therefore, our contribution is two-fold: it gives a modeling of the data that incorporates time and structure and it sheds lights on fundamental questions on the interplay between transactions and social ties, in the \(\breve {G}1\) system. These insights are important for progress in several areas, like in particular the inference of social networks from interaction traces.
This paper is organized as follows. “The \(\breve {G}1\) cryptocurrency” section introduces the \(\breve {G}1\) cryptocurrency and explains the main ideas and mechanisms behind it. In “Dataset and link stream modeling” section, we present the dataset under study and show how link streams model interactions from this dataset. In “Overview of certification and transaction streams” section, we use time series and static graph concepts to give a first insight on the global structure and dynamics of the system. In “How do new certifications and transactions appear between members?” section we consider time and structure together but stay at a basic link level in order to understand the interplay between social ties and transactions. Finally, in “Certifications and transactions neighborhoods” section we use more complex stream concepts mixing time and structure in order to investigate this interplay further.